Centre de recherches mathématiques, Annual Report 1995-1996

Part 6

Theme Year 1996-1997: Combinatorics and Group Theory


The theme year 1996-1997 is devoted to combinatorics and group theory. Besides the CRM Summer School at Banff and the Chaire Aisenstadt, there will be eight workshops and conferences. The members of the scientific committee for this year are: G. Baumslag (CUNY), F. Bergeron (UQAM), N. Bergeron (York), G. Brassard (Montréal), C.J. Colbourn (Water loo), C. Crépeau (Montréal), R. Couture (Montréal), P. Flajolet (INRIA, Rocquencourt), A. Garsia (UCSD), S.M. Gersten (Utah), E. Ghys (Lyon), D. Gildenhuys (McGill), G. Hahn (Montréal), O. Kharlampovich (Mc Gill), D. Krob (Paris VI), G. Labelle (UQAM), C. Lam (Concordia), P. L'Écuyer (Montréal), P. Leroux (UQAM), R.C. Mullin (Waterloo), H. Niederreiter (Austrian Academy of Sciences), C. Reutenauer (UQAM), A. Rosa (McMaster), G. Sabidussi (Montréal), R.P. Stanley (M.I.T.), D.R. Stinson (Nebraska -Lincoln), L. Vinet (Montréal), D. Zeilberger (Philadel phia), E. Zelmanov (Yale).

The scientific events are described below. They will take place at the CRM unless specified otherwise.

Workshop on Pseudorandom Number Generation

3-28 June 1996
Org.:G. Brassard (Montréal), C. Crépeau (Montréal), R. Couture (Montréal), P. L'Écuyer (Montréal), H. Niederreiter (Austrian Academy of Sciences)

The main goal of this workshop is to bring together researchers interested in theoretical and practical aspects of (pseudo-)random number generation by computer. The workshop is spread over a period of 4 weeks. The general theme is the development of practical random number generation software for different classes of applications, such as simulation, statistics, numerical analysis, games, cryptography, etc. The main subjects to be discussed are linear-type methods, nonlinear methods, statistical tests, cryptographically secure generators, parallel generators and efficient software implementations. Within the general theme, each week will have a special subject interest, as follows:

  1. requirements for good generators, randomness criteria and statistical tests in general (June 3-7),
  2. linear methods (June 10-14),
  3. nonlinear methods and cryptographically secure generators (June 17-21),
  4. parallel generators and practical software implementations (June 24-28).

The list of invited speakers includes: A. Compagner, R. Couture, C. Crépeau, E.C. Dudewicz, G. Fishman, M. Fushimi, P. Hellekalek, F. James, G. Larcher, P. L'Écuyer, G. Marsaglia, M. Mascagni, M. Matsumoto, H. Niederreiter, I.M. Sobol', S. Tezuka, I. Vattulainen.

CRM Summer School on Group Theory

Banff Centre of Arts, Banff, Alberta
11-23 August 1996
Org.:G. Baumschlag (CUNY), D. Gildenhuys (McGill), O. Kharlampovich (McGill), E. Zelmanov (Yale)

The summer school will be aimed primarily at Ph.D. students in their final years and recent Ph.D.'s. Its main objective will be to prepare people for the workshops to follow. The topics will be: combinatorial and geometric group theory, hyperbolic and automatic groups, actions of groups on trees, connections between groups and Lie algebras, pro-p-groups, group representations (aimed particularly at the combinatorialists).

The list of invited lecturers includes: G. Baumslag, I. Chiswell, M. du Sautoy, S. Gersten, N. Gupta, K. Gupta, S. Ivanov, O, Kharlampovich, Yu. Kuz'min, A. Myasnikov, M. Sapir, E. Zelmanov.

Workshop on Cayley Graphs

16-21 September 1996
Org.:G. Hahn (Montréal), G. Sabidussi (Montréal)

Cayley graphs of finite and infinite groups will be explored from the point of view of the central role which they play in the general theory of transitive graphs, as well as for the applications which have been found in recent years in the design of interconnecting networks. Specific topics will include combinatorial properties related to the communication of information in Cayley graphs, isomorphism and homomorphism problems, graphs with groups of polynomial growth.

The list of invited speakers includes: N. Alon, B. Alspach, L. Babai, P. Cameron, M.J. Dunwoody, Y. Hamidoune, W. Imrich, S. Klavzar, A. Lubotzky, D. Marusic, B. Mohar, N. Seifter, J. Sirán, V. Trofimov, M.E. Watkins, W. Woess.

Workshop on Hyperbolic and Automatic Groups; Groups Acting on R-Trees

13-24 October 1996
Org.:G. Baumschlag (CUNY), D. Gildenhuys (McGill), O. Kharlampovich (McGill), E. Zelmanov (Yale)

This workshop will bring together international experts in the indicated fields.

The list of invited speakers includes: M. Bestvina, S. Gersten, I. Kapovich, G. Levitt, A. Olshanskii, E. Rips, Z. Sela, H. Short, M. Staretz.

Workshop on Distance-Regular Graphs

18-23 November 1996
Org.:G. Hahn (Montréal), G. Sabidussi (Montréal)

The workshop is intended to cover recent developments in all aspects of the theory of distance-regu lar graphs. One of the major themes will be distance -transitive graphs and problems concerning their clas sification and connections with group theory.

The list of invited speakers includes: E. Bannai, N. Biggs, A.E. Brouwer, P. Cameron, A. Cohen, A.D. Gardiner, C. Godsil, A.A. Ivanov, L.K. Jørgensen, M. Mulder, J. Saxl, P. Terwilliger.

Workshop on General Combinatorial Group Theory

5-16 April 1997
Org.:G. Baumschlag (CUNY), D. Gildenhuys (McGill), O. Kharlampovich (McGill), E. Zelmanov (Yale)

This workshop will include a wide variety of topics in Combinatorial Group Theory, in particular, invariants of infinite groups, profinite groups and constructive aspects of pro-p-groups, exponential groups, language theory, connections between groups and Lie algebras, group actions on non-archimedean trees.

The list of invited lecturers includes: H. Bass, G. Baumslag, R. Grigorchuk, M. Gromov, A. Krasilnikov, G. Labute, A. Lubotzky, J. McCool, A. Myasnikov, Remeslennikov, L. Ribes, A. Shmelkin.

Workshop on Tranversal Designs and Orthogonal Arrays

University of Waterloo, Waterloo, Ontario, April 1997
Org.:C.J. Colbourn (Waterloo), R.C. Mulin (Waterloo), A. Rosa (McMaster), D.R. Stinson (Nebraska-Lincoln)

As combinatorial design theory has matured, certain central objects have been found to play a key role not only in the construction of designs, but also in their application. Transversal designs (equivalently, orthogonal arrays) occupy a fundamental place in the construction of almost all types of designs, primarily as a result of Wilson's existence theory for designs. A central question in combinatorial design theory is therefore the existence of transversal designs. A one week workshop on the subject is planned for April 1997 and the following five main themes will be covered: finite geometry and difference sets, orthogonal arrays in coding theory, incomplete transversal designs, orthogonal arrays and experimental design, applications of transversal designs in design theory.

The list of speakers includes: J. Abel, F. Bennett, J. Bierbrauer, A. Brouwer, A. Bruen, J. Dinitz, J. Doyen, S. Hedayat, K. Heinrich, D. Jungnickel, D. Kreher, C. Laywinve, G. Mullen, N. Sloane, D. Street, V. Tonchev, J. van Rees, R. Wilson, M. Wojtas, L. Zhu.

Workshop on Experimental Mathematics and Combinatorics

19-30 May 1997
Org.:F. Bergeron (UQAM), G. Labelle (UQAM), P. Leroux (UQAM)

Computer algebra methods play an increasingly important role in mathematics. This is particularly true in areas like combinatorics where mathematical experiment is an integral part of any research activity. The goal of this workshop is to survey recent developments in computer algebra as a research tool in mathematics and to work on specific applications primarily in combinatorics. The workshop will consist of one week of invited talks (May 19-23, 1997) followed by one week of informal working sessions.

The list of invited speakers includes: J. Borwein, P. Borwein, P. Flajolet, T. Guttmann, B. Salvy, D. Stanton, V. Strehl, G.X. Viennot, D. Zeilberger, M. Petkovsek

Workshop on Algebraic Combinatorics

9-20 June 1997
Org.:F. Bergeron (UQAM), N. Bergeron (York), C. Reutenauer (UQAM)

The purpose of the workshop is to study interactions between Algebraic Combinatorics and Symmetric Functions, with special emphasis on Descent Algebras of Coxeter groups in relation to quasi-symmetric functions and non-commutative symmetric functions, and on doubly parametrized (Macdonald) (q,t)-symmetric functions, in relation to harmonics of reflection groups.

The list of speakers includes: P. Diaconis*, A. Garsia, I. Gessel, I. Goulden*, M. Haiman, I.G. Macdonald, C. Procesi, L. Solomon, R.P. Stanley, J.Y. Thibon. (The asterisk * indicates a speaker yet to be confirmed.)

Chaire Aisenstadt

Professor László Babai will be giving the first part of the André-Aisenstadt Lectures at the CRM in conjunction with the workshops on Cayley Graphs and on Distance-Regular Graphs in September and November 1996. Fields Medal (1994) winner Professor Efim Zelmanov will hold the second part of the Chaire Aisenstadt, and will be delivering a series of lectures on Combinatorial Algebra in March 1997.

Theme Year 1997-1998: Statistics


The theme year in statistics will emphasize several current directions in the theory and application of statistics, with particular emphasis on problems involving dependent data. Five areas of concentration have been selected: the interface between computation and theoretical statistics, spatial statistics, nonparametric functional estimation, statistical methods in epidemiology and genetic epidemiology, and analysis of longitudinal data.

The members of the advisory committee for the theme year are J.F. Lawless (Waterloo), M. Moore (École Polytechnique), N. Reid (Toronto) and Y. Yatracos (U. de Montréal). The organizers for the concentration programs have been encouraged to emphasize, as much as is feasible, interaction with researchers having special expertise in applications.

Spatial statistics and applications

A great many application areas, such as geology, hydrology, medical imaging, atmospheric science, biology, materials science, and so on, routinely collect large amounts of data that exhibit spatial dependence. Spatial data also raises many interesting inferential problems and statistical methods developed for independent data are rarely applicable. This program plans to explore recently developed methods for particular applications, as well as more general problems of inference.

The program as planned consists of a short course of 20-30 hours to be given over a period of about 3 weeks, to introduce students and others to the general problems and methods of spatial data analysis. This will be followed by four workshops on the topics indicated below.

Image analysis and image restoration

30 March - 3 April 1998
Org.: M. Moore (École Polytechnique)

Statistical inference for spatial processes

6-9 April 1998
Org.: Xavier Guyon (Univ. Paris 1)

Applications in earth and environmental sciences

20-24 April 1998 (tentative)
Org.: R. Lockhart (Simon Fraser)

Statistics of brain mapping

13-14 June 1998
Org.: K. Worsley (McGill)

Functional magnetic resonance imaging is a new and rapidly developing area of medical imaging technology, and there is international expertise in this topic in Montreal. This workshop will follow the 4th International Conference on Functional Mapping of the Human Brain (7-12 June 1998).

Nonparametric functional estimation

Nonparametric functional estimation is widely used in theory and applications, with emphasis usually being on the estimation of density functions, distribution functions, quantile functions, regression functions and nonlinear functionals of the density. Most results to date have been obtained in the framework of independent sampling, but current research directions motivated by applications consider nonparametric functional estimation under various types of dependence.

Nonparametric functional estimation

13-24 October 1997
Org.: Luc Devroye (McGill), George Roussas (U.C. Davis), Yannis Yatracos (Univ. de Montréal)

Statistical methods in epidemiology and genetic epidemiology

Much work in epidemiology is descriptive, but there is considerable recent interest in emphasizing techniques of statistical inference in epidemiology. This program will invite several internationally known re searchers to discuss various aspects of statistical meth ods in epidemiology. The program will consist of a two-week conference, with emphasis in the first week on epidemiology and in the second week on genetic epidemiology. Each topic will have two or three themes with an associated substantive researcher re sponsible for background lectures.

Statistics and epidemiology

3-9 May 1998
Org.: Gerarda Darlington (Toronto), Shelley Bull (Toronto)

Recent developments in descriptive epidemiology, etiologic studies, and clinical epidemiology.

Genetic epidemiology

9-16 May 1998
Org.: Gerarda Darlington (Toronto), Ken Morgan (McGill)

A discussion of statistical and genetic principles (segregation analysis, linkage analysis, association analysis, population genetics, isolate populations, linkage disequilibrium mapping); complex pedigrees and complex traits (gene identity by descent - families, gene identity by descent - individuals).

Longitudinal data analysis

Data collected on the same subjects over time arise frequently in biological applications, and there is a considerable new body of work on models and methods for this type of data. This workshop will provide a survey of recent work, and a discussion of open prob lems in the area. The emphasis will be on applications, and participants are encouraged to bring particular applied problems to the attention of the workshop organizers.

Longitudinal data analysis for complex surveys

March 1998 (tentative)
Org.: Michael Hidiroglou, Sylvie Michaud and David Binder (Statistics Canada)

Nonlinear time series

March 1998 (tentative)
Org.: Roch Roy (Univ. Montréal)

Time series analysis continues to be a subject of important interest in statistics since almost every scientific discipline is concerned with data collected over time. This workshop will focus mainly on two topics of recent and growing interest: resampling methods and the application of wavelets. In many cases, the related results are applicable to both linear and non linear time series.

Event history analysis

25-29 May 1998
Org.: Richard Cook and Jerry Lawless (Waterloo)

Event history analysis is now commonly applied in most branches of science, including demography, epidemiology, medicine, engineering and economics. The purpose of this workshop is to stimulate a critical appraisal of existing models and techniques and to consider future developments.

Theoretical statistics and computation: the interface

Advances in computing power are not only influencing the practice of statistics, but are also influencing the development of theoretical statistics. Computationally intensive techniques such as the bootstrap and Monte Carlo Markov Chain (MCMC) algorithms provide alternatives to inferential approximations developed using asymptotic theory. The application of MCMC techniques to Bayesian analysis of relatively complex problems has provided new impetus for development of standard priors. The wide availability of symbolic computation has also influenced the types of inference problems that can be tackled.

This program will consist of three periods of concentration, each of approximately two weeks, in the areas given below. The format for each period of concentration will consist of a week of background lectures for students and participants, followed by a week long research workshop.

Using the bootstrap for model selection

14-20 September 1997
Org.: Christian Léger (Univ. de Montréal)

Symbolic computation

21-27 September 1997
Org.: James Stafford (Western Ontario)

Empirical Bayes and likelihood inference

9-15 November 1997
Org.: Ejaz Ahmed (Regina), Nancy Reid (Toronto)

CRM Summer School on Likelihood and Asymptotics

1-11 August 1997, Banff
Org.: Tom DiCiccio (Cornell)

Aisenstadt Lectures

Professor Peter Hall of the Australian National University in Canberra and Sir David Cox of Oxford University have accepted invitations to serve as Aisenstadt Lecturers in October 1997 and May 1998 respectively.

Interaction with the Fields Institute

John Chadam has expressed enthusiastic support for having the Fields Institute sponsor activities in statistics and is happy to tie that in with the theme year if that seems appropriate. He has also been independently in contact with Jack Kalbfleisch at Waterloo to discuss a program in Industrial Statistics at the Fields Institute and is willing to work that into the theme year.

Updated information about the schedule and speakers may be obtained from Nancy Reids' web page www.utstat.toronto.edu/reid/crm/.

Theme Year 1998-1999: Number Theory


The year 98-99 will be devoted to number theory. The organizing committee is M. Ram Murty (McGill and Queen's, scientific director), Henri Darmon (Mc Gill) ), Mark Goresky (Institute for Advanced Study), Fiona Murnaghan (Toronto), V. Kumar Murty (Toronto). The focus will be on the four following areas of number theory.

  1. Algebraic cycles and Shimura varieties
  2. Elliptic curves and automorphic forms
  3. p-adic representations
  4. Analytic theory of automorphic L-functions

Each of these areas will be studied by means of a seminar course given by members of the organizing committee. This seminar course will be aimed primarily at graduate students and postdoctoral fellows. The course will be supplemented by a one-week workshop where specialists will lecture on the latest developments. Most likely, the topics (i) and (ii) will be treated by K. Murty, H. Darmon, and M. Goresky in the first term. Topics (iii) and (iv) will be covered by F. Murnaghan and R. Murty respectively in the second term. In one or more of these areas, it is proposed to have some lecture notes published in the CRM series.

In addition, there will be a summer school in Banff, Alberta on Algebraic Cycles, June 7-19, 1998, organized by J. Lewis (Alberta), N. Yui (Queens's) and B. Gordon (Oklahoma). The following have so far agreed to speak at the summer school: S. Bloch (Chicago), J.-L. Colliot-Thélène (CNRS), M. Green (UCLA), U. Jannsen (Cologne), B. Lawson (SUNY), D. Ramakrishnan (Caltech), S. Saito (Tokyo), D. Zagier (Max Planck Institut). Several other speakers have been invited.

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